Methods and apparatus for calibrating CT x-ray beam tracking loop

ABSTRACT

The present invention is, in one embodiment, a method for determining tracking control parameters for positioning an x-ray beam of a computed tomography imaging system having a movable collimator positionable in steps and a detector array including a plurality of rows of detector elements. The method includes steps of obtaining detector samples at a series of collimator step positions while determining a position of a focal spot of the x-ray beam; determining a beam position for each detector element at each collimator step utilizing the determined focal spot positions, a nominal focal spot length, and geometric parameters of the x-ray beam, collimator, and detector array; and determining a calibration parameter utilizing information so obtained. For example, in determining a target beam position at which to maintain the x-ray beam, a detector element differential error is determined according to ratios of successive collimator step positions; and a target beam position is selected for an isocenter element in accordance with the determined element differential errors.

BACKGROUND OF THE INVENTION

[0001] This invention relates generally to computed tomography (CT)imaging and, more particularly, to methods and apparatus for calibrationof z-axis tracking loops for positioning a CT x-ray beam of amulti-slice CT imaging system.

[0002] In at least one known computed tomography (CT) imaging systemconfiguration, an x-ray source projects a fan-shaped beam which iscollimated to lie within an X-Y plane of a Cartesian coordinate systemand generally referred to as the “imaging plane”. The x-ray beam passesthrough the object being imaged, such as a patient. The beam, afterbeing attenuated by the object, impinges upon an array of radiationdetectors. The intensity of the attenuated beam radiation received atthe detector array is dependent upon the attenuation of the x-ray beamby the object. Each detector element of the array produces a separateelectrical signal that is a measurement of the beam attenuation at thedetector location. The attenuation measurements from all the detectorsare acquired separately to produce a transmission profile.

[0003] In known third generation CT systems, the x-ray source and thedetector array are rotated with a gantry within the imaging plane andaround the object to be imaged so that the angle at which the x-ray beamintersects the object constantly changes. A group of x-ray attenuationmeasurements, i.e., projection data, from the detector array at onegantry angle is referred to as a “view”. A “scan” of the objectcomprises a set of views made at different gantry angles, or viewangles, during one revolution of the x-ray source and detector. In anaxial scan, the projection data is processed to construct an image thatcorresponds to a two-dimensional slice taken through the object. Onemethod for reconstructing an image from a set of projection data isreferred to in the art as the filtered back projection technique. Thisprocess converts the attenuation measurements from a scan into integerscalled “CT numbers” or “Hounsfield units”, which are used to control thebrightness of a corresponding pixel on a cathode ray tube display.

[0004] In a multi-slice system, movement of an x-ray beam penumbra overdetector elements having dissimilar response functions can cause signalchanges resulting in image artifacts. Opening system collimation to keepdetector elements in the x-ray beam umbra can prevent artifacts butincreases patient dosage. Known CT systems utilize a closed-loop z-axistracking system to position the x-ray beam relative to a detector array.It would be desirable to provide improved methods and apparatus forcalibration of such systems. In particular, it would be desirable toprovide improved methods and apparatus for determining calibrationparameters such as: (1) a target beam position at which to maintain thex-ray beam; (2) a transfer function to convert sensed trackinginformation into a beam position in millimeters; and (3) valid limits ofthe transfer function.

BRIEF SUMMARY OF THE INVENTION

[0005] There is therefore provided, in one embodiment, a method fordetermining tracking control parameters for positioning an x-ray beam ofa computed tomography imaging system having a movable collimatorpositionable in steps and a detector array including a plurality of rowsof detector elements. The method includes steps of obtaining detectorsamples at a plurality of collimator step positions while determining aposition of a focal spot of the x-ray beam; determining a beam positionfor each detector element at each collimator step utilizing thedetermined focal spot positions, a nominal focal spot length, andgeometric parameters of the x-ray beam, collimator, and detector array;and determining a calibration parameter utilizing information soobtained. For example, in determining a target beam position at which tomaintain the x-ray beam, the method also includes steps of determiningan detector element differential error according to ratios of successivecollimator step positions; and selecting a target beam position for anisocenter element in accordance with the determined element differentialerrors.

[0006] The above described system provides improved tracking calibrationfor CT imaging systems utilizing z-axis tracking loops for positioningx-ray beams.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007]FIG. 1 is a pictorial view of a CT imaging system.

[0008]FIG. 2 is a block schematic diagram of the system illustrated inFIG. 1.

[0009]FIG. 3 is a schematic view of a portion of the CT imaging systemshown in FIG. 1 showing an embodiment of a z-axis position system of thepresent invention.

[0010]FIG. 4 is a flow diagram an embodiment of a z-axis tracking loopof the present invention.

[0011]FIG. 5 is a flow diagram of a method for calibrating tracking loopparameters.

DETAILED DESCRIPTION OF THE INVENTION

[0012] Referring to FIGS. 1 and 2, a computed tomograph (CT) imagingsystem 10 is shown as including a gantry 12 representative of a “thirdgeneration” CT scanner. Gantry 12 has an x-ray source 14 that projects abeam of x-rays 16 toward a detector array 18 on the opposite side ofgantry 12. Detector array 18 is formed by detector elements 20 thattogether sense the projected x-rays that pass through an object 22, forexample a medical patient. Each detector element 20 produces anelectrical signal that represents the intensity of an impinging x-raybeam and hence the attenuation of the beam as it passes through patient22. During a scan to acquire x-ray projection data, gantry 12 and thecomponents mounted thereon rotate about a center of rotation orisocenter 24.

[0013] Rotation of gantry 12 and the operation of x-ray source 14 aregoverned by a control mechanism 26 of CT system 10. Control mechanism 26includes an x-ray controller 28 that provides power and timing signalsto x-ray source 14 and a gantry motor controller 30 that controls therotational speed and position of gantry 12. A data acquisition system(DAS) 32 in control mechanism 26 samples analog data from detectorelements 20 and converts the data to digital signals for subsequentprocessing. An image reconstructor 34 receives sampled and digitizedx-ray data from DAS 32 and performs high-speed image reconstruction. Thereconstructed image is applied as an input to a computer 36 that storesthe image in a mass storage device 38.

[0014] Computer 36 also receives commands and scanning parameters froman operator via console 40 that has a keyboard. An associated cathoderay tube display 42 allows the operator to observe the reconstructedimage and other data from computer 36. The operator supplied commandsand parameters are used by computer 36 to provide control signals andinformation to DAS 32, x-ray controller 28 and gantry motor controller30. In addition, computer 36 operates a table motor controller 44 thatcontrols a motorized table 46 to position patient 22 in gantry 12.Particularly, table 46 moves portions of patient 22 through gantryopening 48.

[0015] In one embodiment, and as shown in FIG. 3, x-ray beam 16 emanatesfrom a focal spot 50 of x-ray source 14 (FIG. 2). X-ray beam 16 iscollimated by collimator 52, and collimated beam 16 is projected towarddetector array 18. Detector array 18 is fabricated in a multi-sliceconfiguration and includes detector element rows 54, 56, 58 and 60 forprojection data collection. A plane 86, generally referred to as the“fan beam plane”, contains the centerline of focal spot 50 and thecenterline of beam 16. Fan beam plane 86 is illustrated in FIG. 3 asbeing aligned with a centerline D₀ of detector array 18, although fanbeam plane 86 will not always be so aligned. Detector element rows 62,64, 66 and 68 serve as z-position detectors for determining a z-axisposition of x-ray beam 16. In one embodiment, detector rows 62, 64, 66,and 68 are rows of detector array 18. Outer rows 62 and 68 are selectedto be at least substantially within penumbra 70 of beam 16. Inner rows64 and 66 are selected to be at least substantially within umbra 72 ofbeam 16. “At least substantially within” means either entirely within orat least sufficiently within so that outer row 62 and 68 signalintensities depend on an x-ray beam position and inner row 64 and 66signal intensities provide references against which outer row signalsare compared. In one embodiment, collimator 52 includes tapered cams 74and 76. (Where it is stated herein that a cam “has a taper,” it is notintended to exclude cams having a taper of zero unless otherwisestated.) X-ray controller 28 controls positioning of cams 74 and 76.Each cam can be independently positioned to alter position and width ofx-ray umbra 72 relative to an edge (not shown) of detector array 18.

[0016] As shown in FIG. 4, one embodiment of a closed-loop method forpositioning beam 16 comprises comparing signals representative of x-rayintensity received from different rows of detector elements andpositioning an x-ray beam in accordance with results of the comparison.In one embodiment, signals representative of x-ray intensity fromdetector rows 62, 64, 66 and 68 are summed 78 to obtain row sums. Thesummation is over views taken in a 20-millisecond interval. For example,after the analog signals are converted to digital format, hardwarecircuitry (not shown) in DAS 32 performs offset correction anddetermines row sums from signals received from outer row 62 and frominner row 64. A corrected ratio R is determined 80 by determining aratio of a sum of signals received from outer row 62 to a sum of signalsreceived from inner row 64 and multiplying the ratio by a ratiocorrection factor. The ratio correction factor, determined from imagingsystem 10 calibration, accounts for different relative DAS gains betweenouter row 62 and inner row 64.

[0017] Beam position Z(R) then is determined 82, in millimeters relativeto a centerline. Beam position Z is obtained by applying a predeterminedbeam position transfer function to the corrected ratio to calculate thex-ray beam position. The beam position transfer function Z(R) isrepresented, for example, by a fourth-degree polynomial havingpredetermined coefficients:

Z(R)=a+bR+cR ² +dR ³ +eR ⁴

[0018] Beam position transfer function Z(R) and its limits are specifiedat imaging system 10 calibration.

[0019] A new collimator position is then determined 84. A focal spotposition ƒ is determined 84 from beam position Z, current collimatorposition C and other system 10 geometric parameters in accordance with:$f = {\frac{\left( {Z - C - T_{s}} \right)}{{fm}_{zz}\left( l_{fs} \right)} + C + T_{s}}$

[0020] where T_(z) represents a current taper of cam 74, ƒm_(zz)represents a focal spot magnification factor at rows 62 and 64 and is afunction of focal spot size, and l_(ƒs) represents focal spot 50 length.A new position for collimator 52 then is determined 84 for a detectorelement 20 positioned toward isocenter 24. Collimator 52 is repositionedwhere an edge (not shown) of collimator 52 would meet a line betweenfocal spot position f and a target beam position Z_(l) which has beenspecified at imaging system 10 calibration. New collimator positionC_(n)thus is determined in accordance with:$C_{n} = {{\frac{\left( {Z_{i} - f} \right)}{{cm}_{i}\left( l_{fs} \right)}z} + f}$

[0021] where cm_(i) represents a current collimator magnification factorat detector element 20 positioned toward isocenter 24 and is a functionof focal spot size, and l_(ƒs) represents focal spot 50 length.

[0022] In one embodiment, steps 78, 80, 82, and 84 are performedindependently for each side of collimator 52 at intervals tocontinuously obtain new positions for each side of collimator 52. Theseintervals are, in one embodiment, 20 milliseconds, to sample the x-raybeam 16 position 25 times during a 0.5 second scan to minimize controlloop lag error. However, in other embodiments, the interval is between 5milliseconds and 50 milliseconds. In still other embodiments, theinterval is between a minimum value sufficient to avoid effects ofquantum noise and high frequency variation (such as due to x-ray tubeanode movement at a run frequency between 50 Hz and 160 Hz) and amaximum contrained by a slew rate of the sag curve. Sampling thechanging sag curve frequently avoids excessive positioning error. (Sagis a periodic movement of x-ray beam 16 resulting from gravity and fromcentrifugal forces acting on mechanical structure during a rotation ofgantry 12.)

[0023] During patient scanning, z-position detectors 62, 64, 66 or 68may become blocked by patient clothing, blankets, or other object. Afterblockage of a z-position detector 62, 64, 66, or 68 has been detected,or when x-ray source 14 first turns on, the loop sample interval isadjusted downward. In one embodiment, the loop sample interval isadjusted downward to 5 milliseconds. After 4 milliseconds ofstabilization, the position of the beam is measured and collimatorpositioning is started to further minimize initial position errors.

[0024] During a blockage, loop operation is suspended. To determine ifany z-position detectors are blocked, a signal from a last data detectorelement 90 adjacent a z-position detector 62, 64, 66 or 68 is comparedto an expected signal Sx. Z-position detector blockage is assumed, inone embodiment, if a last data detector element 20 signal is less than0.9 times expected signal Sx. In other embodiments, detector blockage isassumed when a last data detector element 20 signal is less than a valuebetween 0.95 and 0.5 times expected signal Sx. (It is desirable to makethis value as large in magnitude as possible to identify patientblockage as quickly as possible, thereby avoiding mispositioning ofx-ray beam 16 due to corrupted Z-measurement data. A maximum of 0.95 isused in one embodiment because it is known that x-ray scatter blockagefrom large patients 22, for example, can reduce a signal to 0.95 timesthe expected value.) During a blockage, collimator positioning issuspended. However, position measurement continues at an interval thatis decreased from 20 to 5 milliseconds. The decreased measurementinterval allows imaging system 10 to more quickly detect an end of theblockage and to resume closed-loop positioning.

[0025] Expected signal Sx is written as:

Sx=gmA*csƒ*t*g,

[0026] where gmA is a generator current mA signal proportional to anx-ray source 14 energizing current, csƒ is a scale factor determined atsystem 10 calibration, t is a DAS sample time period, and g is a gainfactor. Gain factor g allows expected signal Sx to be adjusted accordingto a gain value used for scanning. In one embodiment, this gain value isselectable from a plurality of gain values available in system 10.

[0027] In one embodiment, closed loop tracking is suspended when signalcorruption is detected. Signal corruption is detected, for example, bydetermining an actual focal spot length from a beam position and acollimator position, and comparing the actual focal spot length to anominal focal spot length. When a difference of, for example, more than0.1 millimeter is detected between the actual focal spot length and thenominal spot length, corruption is assumed to exist and collimatorpositioning is suspended. (In other embodiments, a difference thresholdfor assuming corruption is as small as 0.05 millimeter or as large asabout 0.6 millimeter. In still other embodiments, a value is selectedbetween a lower limit set by higher probabilities of false activationdue to noise, x-ray scatter and/or momentary beam position disturbancesand an upper limit that still provides some of the advantages oftracking.) However, beam position measurement continues at a decreasedinterval, as when a blockage is detected. Such corruption may occur, forexample, for a short time just prior to or just following detection of apatient blockage. If the corruption persists, for example, over 90° ofrotation of gantry 12 without detecting a patient blockage, amalfunction of the tracking system requiring servicing has likelyoccurred. In such an event, a scan is immediately aborted to avoidpatient dose and collection of non-diagnostic quality images. In otherembodiments, a limit is set from as little as 45° to as much as 360° ofa rotation of gantry 12. In other embodiments, a limit is set between avalue at which a false alarm rate due to scatter and/or an occasionalexceptionally long partial patient 22 blockage is acceptable and anupper limit representing a design choice as to how long compromisedoperation (high dose and/or non-diagnostic quality images) can betolerated before terminating a scan.

[0028] After system 10 has been switched off, position of focal spot 50changes as source 14 cools over time. In one embodiment, before system10 is switched on again, an initial focal spot position is approximatedfrom information obtained when a focal spot position was last measured.An approximation of a linear function is used to model focal spotposition change during cooling in one embodiment, and in anotherembodiment, the linear function is a 97 nanometer per second linearfunction. Because position change with cooling is an exponentialfunction, the linear approximation is clamped at 0.15 millimeters. Thisclamping corresponds to approximately 20% of a cooling change in system10 when fully cold, where a linear approximation to the exponentialfunction suffices. A fully cold position requires 8 to 12 hours withoutpatient scanning, and a tube warm up prior to patient scanning isnormally requested if the tube has been off more than 1 hour. Therefore,a fully cold position, although possible, is not likely during normalpatient scanning. During tube warm up a current measured position of thefocal spot is established again for initial positioning of thecollimator.

[0029] Several tracking loop parameters described herein, specifically,beam position transfer function Z(R) and its limits and target beamposition Z_(l), are determined at system 10 calibration. FIG. 5illustrates one embodiment of a method for calibrating tracking loopparameters. In this embodiment, data from a stationary sweep scan iscollected 100 while collimator 52 is stepped through a sequence ofz-axis positions. Beam 16 is incremented 0.3 millimeters on detectorarray 18 exposure surface for each collimator 52 step position. Thesweep scan data is offset-corrected and view averaged 102 to obtain aset of detector samples for each collimator 52 step position. A positionof the focal spot is then determined 104. A collimator 52 z-axisposition offset from detector array centerline D₀ is determined 104, asthe point where outer rows 62 and 68 receive signals of half-maximumintensity at full detector element 20 width. Position of focal spot 50during sweep scan then is determined 104 from collimator 52 z-axisoffset and nominal system 10 geometric parameters.

[0030] A beam 16 position is determined 106 for each detector element 20at each collimator 52 step position. Beam 16 positions are determinedfrom sweep scan focal spot 50 position, nominal length of focal spot 50,and nominal system 10 geometry.

[0031] Target beam position Z_(l) then is determined 108 for detectorelement 20 positioned toward isocenter 24. When beam 16 is directed attarget beam position Z_(l), beam 16 is sufficiently close to detectorarray 18 edge 92 to prevent imaging artifacts but is far enough away tominimize patient dosage. To determine target beam position Z_(l), ratiosof detector samples for successive collimator 52 step positions areutilized to determine a detector differential error. A reconstructionerror sensitivity function w(i) then is applied to weight the detectordifferential error. Reconstruction error sensitivity function w(i) isrelated to the percent positive contribution of a detector element 20 asa function of its radial distance from isocenter 24. Function w(i), inone embodiment, is computed from nominal system geometry. In anotherembodiment, w(i) is empirically determined. For example, the followingequations describe an empirical determination of w(i):

b(i)=0.018, 0≦i≦5

b(i)=0.035+0.00075 x(i−5), 5≦i≦213

b(i)=0.414+0.00365x(i−213),214≦i≦n

[0032] where i represents detector element position from isocenter 24and b(i) represents an artifact threshold, i.e. a percent differentialerror, for a double detector element 20 error. Reconstruction errorsensitivity function w(i) then is determined in accordance with:

w(i)=0.18/b(i).

[0033] A collimator 52 step position SP is determined for which theweighted detector differential error exceeds a limit L empirically knownto produce image artifacts, for example, 0.04 percent. Target beamposition Z_(l) then is set for the isocenter detector element at adistance just preceding SP by an amount exceeding applicable trackingloop positioning error.

[0034] Beam position transfer function Z(R) then is determined 110 for aratio R of an average of outer row 62 to inner row 64 signals for a setof detector elements at an extreme end of x-ray fan beam 16. Beam 16positions, determined 106 for each collimator 52 step position, arefitted to the ratio for each collimator 52 step position with afourth-degree polynomial, for example, in accordance with:

Z(R)=a+bR+cR ² +dR ³ +eR ⁴

[0035] over a suitable ratio range between a maximum and minimum for thesequence of steps.

[0036] A valid position measurement range for Z(R) is determined 112 asbetween end limits of the set of collimator 52 step positions for whichan error between a beam 16 position determined by Z and an actual beam16 position is less than a predetermined limit, for example, 0.2millimeters. In other embodiments, the predetermined limit is between0.1 millimeters to 0.6 millimeters. In still other embodiments, thepredetermined limit is set at a value between a lower limit just above avalue at which a range of beam 16 position that can be preciselymeasured is too limited, and just below a lower limit that is deemed tocreate tracking errors so large as to unacceptably compromise thebenefits of tracking.

[0037] The above-described tracking loop senses the signal ratio betweendetector rows and moves system collimation to maintain the x-ray beamvery close to the imaging system detector array edge during patientscanning. As a result, patient x-ray dosage is reduced 20 to 40 percentwithout sacrificing image quality.

[0038] Other functions can be utilized in place of beam positiontransfer function Z(R) and also in place of reconstruction errorsensitivity function w(i).

[0039] In some embodiments, the methods described herein are implementedby software, firmware, or by a combination thereof controlling eithercomputer 36, image reconstructor 34, or both. Also, additionalz-detector rows can be provided. In such an embodiment, variouscombinations of z-detector row signals can be used as the inner andouter row signals, thereby becoming identified as such, or a differentand/or more elaborate transfer function can be used to determine a beamposition.

[0040] The above described calibration methods and apparatus providesimproved calibration for z-axis tracking loops for positioning x-raybeams on multi-slice detectors of CT imaging systems. The methods andapparatus provide a target beam position at which to maintain the x-raybeam, a transfer function to convert detector ratio information into abeam position in millimeters (or other suitable units via conversionfactors), and valid limits of the ratio to beam position transferfunction.

[0041] It should be understood that system 10 is described herein by wayof example only, and the invention can be practiced in connection withother types of imaging systems. Furthermore, it will be recognized bythose skilled in the art that the calibration system described herein isalso useful for other applications which require x-ray beam trackingcalibration, such as for object location or sensing of movement.

[0042] While the invention has been described in terms of variousspecific embodiments, those skilled in the art will recognize that theinvention can be practiced with modification within the spirit and scopeof the claims.

1. A method for determining tracking control parameters for positioningan x-ray beam of a computed tomography imaging system, the imagingsystem including a movable collimator positionable in steps and adetector array including a plurality of rows of detector elements, saidmethod comprising the steps of: obtaining detector samples at aplurality of collimator step positions while determining a position of afocal spot of the x-ray beam; determining a beam position for eachdetector element at each collimator step utilizing the determined focalspot positions, a nominal focal spot length, and geometric parameters ofthe x-ray beam, collimator, and detector array; determining an detectorelement differential error according to ratios of successive collimatorstep positions; and selecting a target beam position for an isocenterelement in accordance with the determined element differential errors.2. A method in accordance with claim 1 wherein the plurality of detectorrows are z-axis detector rows, and the detector array has a centerlineperpendicular to the z-axis, an outer detector row, and an innerdetector row; said determining a position of a focal spot of the x-raybeam comprises the steps of: determining a collimator z-axis positionoffset from the detector array centerline at a point at which outerdetector row signals are reduced to a full width at a half maximum; anddetermining a focal spot position as a function of the determinedcollimator z-axis position and the geometric parameters of the x-raybeam, collimator, and detector array.
 3. A method in accordance withclaim 1 further comprising the step of offset-correcting andview-averaging the obtained detector samples at a plurality ofcollimator step positions to obtain a set of detector samples for eachcollimator step position used in said steps of determining a beamposition transfer function and determining a differential error forselection of the target beam position.
 4. A method in accordance withclaim 1 wherein selecting a target beam position for an isocenterdetector element in accordance with the determined element differentialerrors comprises the steps of: weighting the detector elementdifferential error by a reconstruction error sensitivity function;determining a step position at which the weighted detector elementdifferential error exceeds a predetermined limit; and setting a trackingbeam position for the isocenter detector element at a distance from thedetermined step position preceding a step that exceeds a predeterminedartifact limit by an amount that exceeds a tracking loop positioningerror.
 5. A method in accordance with claim 4 wherein the reconstructionerror sensitivity function is detector element dependent.
 6. A method inaccordance with claim 5 wherein the reconstruction error sensitivityvaries according to a distance of the detector element from an isocenterelement.
 7. A method in accordance with claim 4 wherein the detectorrows have at least 214 elements on each side of an isochannel element,and the reconstruction error sensitivity function is: w(i)=0.18/b(i);where: i=a detector element position from an isocenter detector element;b(i)=an artifact threshold (% differential error) for a double detectorelement error; and b(i)=0.018, 0≦i≦5 b(i)=0.035+0.00075x(i−5), 5≦i≦213b(i)=0.414+0.00365x(i−213), 214≦i≦n.
 8. A method for determiningtracking control parameters for positioning an x-ray fan beam of acomputed tomography imaging system, the imaging system including amovable collimator positionable in steps and a detector array includinga plurality of rows of detector elements including at least an inner rowand an outer row, said method comprising the steps of: obtainingdetector samples at a plurality of collimator step positions whiledetermining a position of a focal spot of the x-ray fan beam;determining a beam position for each detector element at each collimatorstep utilizing the determined focal spot positions, a nominal focal spotlength, and geometric parameters of the x-ray fan beam, collimator, anddetector array; and determining a beam position transfer function for aratio of an average of detector outer row signals to detector inner rowsignals for a set of detector elements at an extreme end of the x-rayfan beam in accordance with a selected approximation over a selectedratio range between a minimum and a maximum ratio for the plurality ofcollimator step positions.
 9. A method in accordance with claim 8wherein determining a beam position transfer function comprises thesteps of fitting, to a polynomial function, the determined beampositions at each step as a function of the ratio of an average ofdetector outer row signals to detector inner row signals,
 10. A methodin accordance with claim 9 wherein the polynomial function is a fourthdegree polynomial.
 11. A method in accordance with claim 8 furthercomprising the step of determining a valid measurement range of thetransfer function as end limits of the plurality of collimator steppositions for which an error between beam positions computed using thetransfer function and an actual beam position is less than apredetermined limit.
 12. A method in accordance with claim 11 whereinthe predetermined limit is between 0.1 millimeters and 0.6 mm.
 13. Amethod in accordance with claim 11 wherein the predetermined limit is0.2 millimeters.
 14. A computed tomography imaging system comprising anx-ray source, a detector array including a plurality of rows of detectorelements, and a movable collimator positionable in steps and configuredto collimate and position an x-ray beam produced by said x-ray source onsaid detector array, said system configured to: obtain detector samplesat a plurality of collimator step positions while determining a positionof a focal spot of the x-ray beam; determine a beam position for eachdetector element at each collimator step utilizing the determined focalspot positions, a nominal focal spot length, and geometric parameters ofthe x-ray beam, collimator, and detector array; determine an detectorelement differential error according to ratios of successive collimatorstep positions; and select a target beam position for an isocenterelement in accordance with the determined element differential errors.15. A system in accordance with claim 14 wherein the plurality ofdetector rows are z-axis detector rows, and the detector array has acenterline perpendicular to the z-axis, an outer detector row, and aninner detector row; and said system being configured to determine aposition of a focal spot of the x-ray beam comprises said system beingconfigured to: determine a collimator z-axis position offset from thedetector array centerline at a point at which outer detector row signalsare reduced to a full width at a half maximum; and determine a focalspot position as a function of the determined collimator z-axis positionand the geometric parameters of the x-ray beam, collimator, and detectorarray.
 16. A system in accordance with claim 14 further configured tooffset-correct and view-average the obtained detector samples at aplurality of collimator step positions to obtain a set of detectorsamples for each collimator step position used in determining saidtarget beam position transfer function and in determining saiddifferential error for selection of said target beam position.
 17. Asystem in accordance with claim 14 wherein said system being configuredto select a target beam position for an isocenter detector element inaccordance with the determined element differential errors comprisessaid system being configured to: weight the detector elementdifferential error by a reconstruction error sensitivity function;determine a step position at which the weighted detector elementdifferential error exceeds a predetermined limit; and set a trackingbeam position for the isocenter detector element at a distance from thedetermined step position preceding a step that exceeds a predeterminedartifact limit by an amount that exceeds a tracking loop positioningerror.
 18. A system in accordance with claim 17 wherein thereconstruction error sensitivity function is detector element dependent.19. A system in accordance with claim 18 wherein the reconstructionerror sensitivity varies according to a distance of the detector elementfrom an isocenter element.
 20. A system in accordance with claim 17wherein the detector rows have at least 214 elements on each side of anisochannel element, and the reconstruction error sensitivity functionis: w(i)=0.18/b(i); where: i=a detector element position from anisocenter detector element; b(i)=an artifact threshold (% differentialerror) for a double detector element error; and b(i)=0.018, 0≦i≦5b(i)=0.035+0.00075x(i−5), 5≦i≦213 b(i)=0.414+0.00365x(i−213), 214≦i≦n.21. A computed tomography imaging system comprising an x-ray source, adetector array including a plurality of rows of detector elements, and amovable collimator positionable in steps and configured to collimate andposition an x-ray beam produced by said x-ray source on said detectorarray, said system configured to: obtain detector samples at a pluralityof collimator step positions while determining a position of a focalspot of the x-ray fan beam; determine a beam position for each detectorelement at each collimator step utilizing the determined focal spotpositions, a nominal focal spot length, and geometric parameters of thex-ray fan beam, collimator, and detector array; and determine a beamposition transfer function for a ratio of an average of detector outerrow signals to detector inner row signals for a set of detector elementsat an extreme end of the x-ray fan beam in accordance with a selectedapproximation over a selected ratio range between a minimum and amaximum ratio for the plurality of collimator step positions.
 22. Asystem in accordance with claim 21 wherein said system being configuredto determine a beam position transfer function comprises the steps offitting, to a polynomial function, the determined beam positions at eachstep as a function of the ratio of an average of detector outer rowsignals to detector inner row signals,
 23. A system in accordance withclaim 22 wherein the polynomial function is a fourth degree polynomial.24. A system in accordance with claim 21 further configured to determinea valid measurement range of the transfer function as end limits of theplurality of collimator step positions for which an error between beampositions computed using the transfer function and an actual beamposition is less than a predetermined limit.
 25. A system in accordancewith claim 24 in which the predetermined limit is between 0.1 and 0.6millimeters.
 26. A system in accordance with claim 24 in which thepredetermined limit is 0.2 millimeters.